Question

The length and width of a rectangle are measured as 27 cm and 50 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

Answer 1

7.7cm

Explanation:

Area of a rectangle is expressed as

A = Length × Width

A = LW

Let dL and dW be the errors in the measurements.

If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.

The area of the rectangle with error will be expressed as A = LdW + WdL

Given L = 27cm and W = 50cm

A = 27(0.1)+50(0.1)

A = 2.7+5.0

A = 7.7cm

Hence, the maximum error in the calculated area of the rectangle is 7.7cm